Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000141
(load all 2 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000141: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [2,1] => [2,1] => [2,1] => 1
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [3,2,1] => [3,1,2] => [2,3,1] => 1
[1,3,2] => [2,3,1] => [3,2,1] => [3,2,1] => 2
[2,1,3] => [3,1,2] => [2,3,1] => [3,1,2] => 2
[2,3,1] => [1,3,2] => [1,3,2] => [1,3,2] => 1
[3,1,2] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => [4,1,2,3] => [2,3,4,1] => 1
[1,2,4,3] => [3,4,2,1] => [4,1,3,2] => [2,4,3,1] => 2
[1,3,2,4] => [4,2,3,1] => [4,3,1,2] => [3,4,2,1] => 2
[1,3,4,2] => [2,4,3,1] => [4,2,1,3] => [3,2,4,1] => 2
[1,4,2,3] => [3,2,4,1] => [4,3,2,1] => [4,3,2,1] => 3
[1,4,3,2] => [2,3,4,1] => [4,2,3,1] => [4,2,3,1] => 3
[2,1,3,4] => [4,3,1,2] => [2,4,1,3] => [3,1,4,2] => 2
[2,1,4,3] => [3,4,1,2] => [2,4,3,1] => [4,1,3,2] => 3
[2,3,1,4] => [4,1,3,2] => [3,4,2,1] => [4,3,1,2] => 3
[2,3,4,1] => [1,4,3,2] => [1,4,2,3] => [1,3,4,2] => 1
[2,4,1,3] => [3,1,4,2] => [3,4,1,2] => [3,4,1,2] => 2
[2,4,3,1] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 2
[3,1,2,4] => [4,2,1,3] => [3,1,4,2] => [2,4,1,3] => 2
[3,1,4,2] => [2,4,1,3] => [3,2,4,1] => [4,2,1,3] => 3
[3,2,1,4] => [4,1,2,3] => [2,3,4,1] => [4,1,2,3] => 3
[3,2,4,1] => [1,4,2,3] => [1,3,4,2] => [1,4,2,3] => 2
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
[3,4,2,1] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[4,1,2,3] => [3,2,1,4] => [3,1,2,4] => [2,3,1,4] => 1
[4,1,3,2] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[4,2,1,3] => [3,1,2,4] => [2,3,1,4] => [3,1,2,4] => 2
[4,2,3,1] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[4,3,1,2] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => [5,1,2,3,4] => [2,3,4,5,1] => 1
[1,2,3,5,4] => [4,5,3,2,1] => [5,1,2,4,3] => [2,3,5,4,1] => 2
[1,2,4,3,5] => [5,3,4,2,1] => [5,1,4,2,3] => [2,4,5,3,1] => 2
[1,2,4,5,3] => [3,5,4,2,1] => [5,1,3,2,4] => [2,4,3,5,1] => 2
[1,2,5,3,4] => [4,3,5,2,1] => [5,1,4,3,2] => [2,5,4,3,1] => 3
[1,2,5,4,3] => [3,4,5,2,1] => [5,1,3,4,2] => [2,5,3,4,1] => 3
[1,3,2,4,5] => [5,4,2,3,1] => [5,3,1,2,4] => [3,4,2,5,1] => 2
[1,3,2,5,4] => [4,5,2,3,1] => [5,3,1,4,2] => [3,5,2,4,1] => 3
[1,3,4,2,5] => [5,2,4,3,1] => [5,4,1,3,2] => [3,5,4,2,1] => 3
[1,3,4,5,2] => [2,5,4,3,1] => [5,2,1,3,4] => [3,2,4,5,1] => 2
[1,3,5,2,4] => [4,2,5,3,1] => [5,4,1,2,3] => [3,4,5,2,1] => 2
[1,3,5,4,2] => [2,4,5,3,1] => [5,2,1,4,3] => [3,2,5,4,1] => 2
[1,4,2,3,5] => [5,3,2,4,1] => [5,4,2,1,3] => [4,3,5,2,1] => 3
[1,4,2,5,3] => [3,5,2,4,1] => [5,4,3,1,2] => [4,5,3,2,1] => 3
[1,4,3,2,5] => [5,2,3,4,1] => [5,3,4,1,2] => [4,5,2,3,1] => 3
[1,4,3,5,2] => [2,5,3,4,1] => [5,2,4,1,3] => [4,2,5,3,1] => 3
[1,4,5,2,3] => [3,2,5,4,1] => [5,3,2,1,4] => [4,3,2,5,1] => 3
Description
The maximum drop size of a permutation. The maximum drop size of a permutation $\pi$ of $[n]=\{1,2,\ldots, n\}$ is defined to be the maximum value of $i-\pi(i)$.
Matching statistic: St000651
(load all 4 compositions to match this statistic)
Mapping
St000651: Permutations ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 92%
Values
[1] => 0
[1,2] => 1
[2,1] => 0
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 1
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 2
[2,1,4,3] => 3
[2,3,1,4] => 3
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 2
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 1
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 2
[1,2,5,3,4] => 3
[1,2,5,4,3] => 3
[1,3,2,4,5] => 2
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 3
[1,4,2,5,3] => 3
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 3
[1,5,6,7,4,2,3] => ? = 4
[1,7,2,6,3,5,4] => ? = 6
[2,3,7,4,6,5,1] => ? = 4
[2,4,6,1,3,5,7] => ? = 2
[2,4,6,3,7,5,1] => ? = 4
[2,4,7,3,6,5,1] => ? = 3
[2,5,4,3,6,1,7] => ? = 6
[2,5,4,6,3,7,1] => ? = 4
[2,5,4,7,3,6,1] => ? = 3
[2,5,6,3,4,7,1] => ? = 3
[2,5,7,3,6,4,1] => ? = 3
[2,6,1,7,3,5,4] => ? = 6
[2,6,1,7,4,3,5] => ? = 6
[2,6,3,5,4,7,1] => ? = 4
[2,6,3,5,7,4,1] => ? = 4
[2,6,3,7,4,5,1] => ? = 4
[2,6,7,3,5,4,1] => ? = 4
[2,7,3,4,5,6,1] => ? = 5
[2,7,3,4,6,5,1] => ? = 5
[2,7,3,5,6,4,1] => ? = 5
[2,7,3,6,4,5,1] => ? = 5
[2,7,3,6,5,4,1] => ? = 5
[2,7,4,5,6,3,1] => ? = 5
[2,7,4,6,5,3,1] => ? = 5
[2,7,5,6,3,4,1] => ? = 5
[2,7,6,3,4,5,1] => ? = 5
[2,7,6,3,5,4,1] => ? = 5
[3,4,5,1,6,2,7] => ? = 5
[3,4,5,1,7,2,6] => ? = 6
[3,5,1,7,2,4,6] => ? = 6
[3,5,1,7,2,6,4] => ? = 6
[3,7,1,6,5,2,4] => ? = 5
[3,7,4,6,5,1,2] => ? = 4
[4,1,5,2,6,3,7] => ? = 4
[4,1,7,3,5,2,6] => ? = 6
[4,1,7,3,6,2,5] => ? = 6
[4,2,1,5,3,6,7] => ? = 4
[4,2,5,7,3,6,1] => ? = 3
[4,2,6,7,3,1,5] => ? = 4
[4,7,3,6,1,5,2] => ? = 4
[4,7,3,6,2,5,1] => ? = 3
[5,2,4,7,3,6,1] => ? = 3
[5,3,1,2,6,4,7] => ? = 4
[5,3,1,4,2,6,7] => ? = 4
[5,3,1,6,4,2,7] => ? = 5
[5,3,1,7,4,2,6] => ? = 6
[5,3,2,1,6,4,7] => ? = 5
[5,3,2,6,4,7,1] => ? = 4
[5,3,7,4,1,2,6] => ? = 4
[5,3,7,4,2,6,1] => ? = 4
Description
The maximal size of a rise in a permutation. This is $\max_i \sigma_{i+1}-\sigma_i$, except for the permutations without rises, where it is $0$.